The game referred to generally as “bingo” is played with predetermined bingo cards that include a number of designations randomly arranged in a grid, matrix, or other layout of spots or locations. The bingo cards may be physically printed on paper or another suitable material, or may be represented by a data structure which defines a bingo card representation having the various card locations and designations associated with the locations. In the traditional bingo game sequence, a number of the predetermined bingo cards are first sold for a particular bingo game. After the sale of bingo cards is closed for a given game, designations are randomly selected from a pool of available designations and matched to the designations on each bingo card that is in play in the bingo game. This matching of bingo designations randomly selected for a game and bingo designations associated with a bingo card in play in the game is commonly referred to as daubing the card. Daubing a card results in an arrangement of matched spots or card locations for the card.
In traditional bingo games, daubing was done manually by the player holding the bingo card, and then by a game administrator to verify a win in the game. More recent bingo gaming systems automatically check for winning patterns on a bingo card as designations are randomly selected for a game. Regardless of how the bingo cards in play in a game are daubed, the first bingo card which is daubed to achieve a predefined game ending pattern is considered a winning card for the game and a prize may be awarded to the player holding the winning card. Other prizes may be awarded for bingo cards achieving other patterns of daubed locations in the course of a bingo game.
One problem with bingo-type games is that the probability of winning or losing with a particular bingo card is always determined by a fixed set of constraints. These constraints include the number of designations available in the pool of designations, the predetermined pattern or patterns to be matched, and the number of locations on the bingo card. For a given set of constraints, the probabilities of winning and losing are generally fixed. Although it is possible to vary these bingo probabilities by varying these constraints, varying the constraints may be cumbersome. Also, even varying the constraints for the bingo game has only a limited effect on the resulting bingo probabilities of winning a prize in a particular bingo game.